What is the integral of (sin(x))/(cos(x)+1) ?

The integral of (sin(x))/(cos(x)+1) is -ln|cos(x)+1|+C

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integral of (sin(x))/(cos(x)+1)

\int \frac{sin ( x )}{cos ( x ) + 1} d x

- ln ∣ cos (x) + 1 ∣ + C

Solution steps

\int \frac{sin ( x )}{cos ( x ) + 1} d x

Apply u-substitution

: \int - \frac{1}{u} d u

= \int - \frac{1}{u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = cos (x) + 1

= - ln ∣ cos (x) + 1 ∣

Add a constant to the solution

= - ln ∣ cos (x) + 1 ∣ + C

(y - y x^{2}) \frac{d y}{d x} = (y + 1)^{2}

f (x) = 24

\frac{\partial}{\partial y} (6 x + 5 y)

(- 3 sin (x) - y sin (x) + 5 cos (x)) d x + cos (x) d y = 0

\int \frac{z}{( z + \frac{1}{2} - \frac{5}{2} ) ( z + \frac{1}{2} + \frac{5}{2} )} d z

What is the integral of (sin(x))/(cos(x)+1) ?
The integral of (sin(x))/(cos(x)+1) is -ln|cos(x)+1|+C